Hyperbolic Functions

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Hyperbolic functions are analogs of trigonometric functions that are based on hyperbolas instead of circles.

acosh() Function

The acosh() function returns inverse hyperbolic cosine of x.

Syntax

math.acosh(x)

Parameters

• x − A positive number >= 1.

Return Value

This function returns a float, corresponding to inverse hyperbolic cosine of x.

Example

from math import acosh

x = 30
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

x = 5.5
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

x = 1
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

x = 0.5
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

x = 45
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

It will produce the following output −

x: 30 acosh(x): 4.0940666686320855
x: 5.5 acosh(x): 2.389526434574219
x: 1 acosh(x): 0.0
Traceback (most recent call last):
   File "C:\Users\mlath\examples\main.py", line 17, in <module>
      val = acosh(x)
            ^^^^^^^^
ValueError: math domain error

asinh() Function

The asinh() function returns the inverse hyperbolic sine value of a positive or negative number.

Syntax

math.asinh(x)

Parameters

• x − a positive or negative number.

Return Value

The asinh() function returns a float that represents inverse hyperbolic sine of x.

Example

from math import asinh

x = 24
val = asinh(x)
print ("x: ",x, "asinh(x): ", val)

x = -12
val = asinh(x)
print ("x: ",x, "asinh(x): ", val)

x = 1
val = asinh(x)
print ("x: ",x, "asinh(x): ", val)

x = 0.5
val = asinh(x)
print ("x: ",x, "asinh(x): ", val)

It will produce the following output −

x: 24 asinh(x): 3.8716347563877314
x: -12 asinh(x): -3.179785437699879
x: 1 asinh(x): 0.881373587019543
x: 0.5 asinh(x): 0.48121182505960347

atanh() Function

The atanh() function in math module returns the inverse hyperbolic tangent of a number.

Syntax

math.tanh(x)

Parameters

• x − a numeric operand for which atanh value is to be calculated. Must be in the range -0.99 to 0.99.

Return Value

The atanh() function returns the inverse hyperbolic tangent of x.

Example

from math import atanh

x = 0.55
val = atanh(x)
print ("x: ",x, "atanh(x): ", val)

x = -0.55
val = atanh(x)
print ("x: ",x, "atanh(x): ", val)

x = 0
val = atanh(x)
print ("x: ",x, "atanh(x): ", val)

x = 1.25
val = atanh(x)
print ("x: ",x, "atanh(x): ", val)

It will produce the following output −

x: 0.55 atanh(x): 0.6183813135744636
x: -0.55 atanh(x): -0.6183813135744636
x: 0 atanh(x): 0.0
Traceback (most recent call last):
   File "C:\Users\mlath\examples\main.py", line 17, in 
   val = atanh(x)
         ^^^^^^^^
ValueError: math domain error

cosh() Function

The cosh() function in math module returns the hyperbolic cosine value of the given number. The value is equivalent to (exp(x) + exp(-x)) / 2.

Syntax

math.cosh(x)

Parameters

• x − a number whose hyperbolic cosine is to be found.

Return Value

The cosh() function returns a float, representing the hyperbolic cosine of x.

Example

from math import cosh

x = 0.55
val = cosh(x)
print ("x: ",x, "cosh(x): ", val)

x = 1
val = cosh(x)
print ("x: ",x, "cosh(x): ", val)

x = 0
val = cosh(x)
print ("x: ",x, "cosh(x): ", val)

x = 6.50
val = cosh(x)
print ("x: ",x, "cosh(x): ", val)

It will produce the following output −

x: 0.55 cosh(x): 1.155101414123941
x: 1 cosh(x): 1.5430806348152437
x: 0 cosh(x): 1.0
x: 6.5 cosh(x): 332.5715682417774

sinh() Function

The sinh() function returns the hyperbolic sine of given number.

Syntax

math.sinh(x)

Parameters

• x − a number whose sinh value is to be computed.

Return Value

The sinh() function returns a float representing the hyperbolic sine of x.

Example

from math import sinh, pi

x = 1
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

x = 12.23
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

x = -12.23
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

x = 0
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

x = pi
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

It will produce the following output −

x: 1 sinh(x): 1.1752011936438014
x: 12.23 sinh(x): 102421.59104557337
x: -12.23 sinh(x): -102421.59104557337
x: 0 sinh(x): 0.0
x: 3.141592653589793 sinh(x): 11.548739357257746

tanh() Function

The tanh() function in math module returns the hyperbolic tangent of a given number.

Syntax

math.tanh(x)

Parameters

• x − a number to calculate the hyperbolic tangent.

Return Value

The tanh() function returns a float number and represents the hyperbolic tangent value of x.

Example

from math import tanh, pi

x = 1
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

x = 12.23
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

x = -12.23
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

x = 0
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

x = pi
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

It will produce the following output −

x: 1 tanh(x): 0.7615941559557649
x: 12.23 tanh(x): 0.9999999999523363
x: -12.23 tanh(x): -0.9999999999523363
x: 0 tanh(x): 0.0
x: 3.141592653589793 tanh(x): 0.99627207622075